Warm-up

Ways to Encourage Persistence

  One of the things we have to work with students is perseverance.  As  you know many of my students are ELL and they find it difficult to continue working on problems and are more likely to give up. 

What are some ways to help students perseverance, so they are less likely to give up and more willing to work their way through the problems.  Unfortunately, research indicates if a student cannot solve a problem within a few minutes, they are more likely to give up.


1.  It is suggested teachers model their own thinking as they solve problems.  This means they talk out loud what is going through their minds as they solve a problem.  This can include discussing being perplexed at one point and sharing what makes it perplexing.  As students see this, they see how to verbalize their own questions.

2. Teachers should also encourage think time.  In other words, students should be allowed time to think about how they are going to solve the problems.  They need time to consider ways to solve the problem so you cannot expect a quick answer.

3.  Encourage students to solving problems using a variety of methods.  By exposing them to a variety of ways, they can choose the method that makes the most sense to them. This also allows them the tools to try different methods if one does not work.

4. Teachers can plan to build persistence.  One way fo doing this is to ask questions such as "Tell me more about it." or "Can you say that in a different way so other understand?" or "Can you put that in your own words."

5. Communicate with students and parents about attitudes on math such as thinking you are not good at math is a learned attitude.   Many parents and students believe the ability to do mathematics is based on talent rather than effort. 

6.  Expect students to share their ideas with others verbally while commenting on others ideas.  They are asked to go to the board to share their ideas and solutions.  They can include representations to show how they see it.

7. Help students realize that it is OK to make mistakes. They should think of mistakes as problems ot be solved or as honing their skills.

I like some of these suggestions and I plan to implement some of them.  I already show students different methods for solving problems but there is more I can do such as verbalize my thinking.  Let me know what you think.

Have a good day.

Ways To Encourage Higher Order Thinking.

  I often wonder how to encourage students to use higher order skills rather than just trying to guess the answer.  I often wonder what techniques I can use to help them.  The textbook has some higher order thinking questions but my students need to have a model on how to do answer them.

I've been working on them with question that may have more than one answer and the justification for their answer but I need more.

Higher order thinking skills are above simple memorization or rote.  It requires them to take the memorized facts to a higher level such as inferring, connecting, manipulating or other such skill.  Suggestions for increasing higher order thinking skills include:

1. Teach the strategies so they know them.

2.  Make sure students understand the important features of one concept that distinguishes it from another.

3. Name the key concept and help students determine the type of concept it is.  Is it concrete, abstract, verbal, nonverbal, or process.

4. Help poorly performing students learn to express themselves by working on verbalizing the steps involved.

5.  Move from concrete to abstract and back so there is a understanding of both.

6. When teaching concepts include false features to help show what its not along with examples of what it is and what its not.

7. Always make sure students have mastered the basic concepts before moving on to the more sophisticated concepts.

8.  Take time to connect concepts beginning with connecting the smaller ones to larger ones.

This two page pdf has some great questions geared to help develop higher order thinking. The questions fall into promoting problem solving, what to do if a student gets stuck, making connections among ideas and applications, encouraging reflections, checking student progress, making sense of mathematics, and encouraging prediction. 

I especially like the questions under helping students when they get stuck. The questions are geared to have students think about the next step.  The questions are such as "How did you tackle a similar problem?" or "Have you compared your work with others in the group?" 

I plan to download these questions to use in class.  I like the questions guide rather than give direct answers.  Check them out and let me know what you think.

Have a good day.

Math Castle

 I downloaded another app designed to help students practice their algebraic skills.  Math Castle has a free version which allows you to access the first level problems for all operations and mixed.  If you like it, you can upgrade to the full version for $1.99.

Once you decide which operation you want to practice, you will be given a page with options for the numbers involved in the problems.
You have a choice of the numbers involved in the problems.  It means the student can start out with easy problems and work up to the problems with larger numbers.

Once the game starts, problems begin to cross the sky in sun like carriers.  the problems are presented in several different ways such as b = 17 -15 or 17 + b = 27 so the student is not always answering questions with the same format.




The way to score gold is to solve the equation, touch the sun so a ball of energy flies down and destroys it if it is the correct answer.  If its wrong, the sun keeps coming but you can try again.

As the student proves their ability, the number of suns increases and begins to arrive faster and faster.  The early ones allow time to use a paper and pencil but as the attack speeds up, it requires the use of mental math to solve the problem.

I found it fun but what I find fun, students do not always find fun.  I am going to have a few students play with it to let me know how they like it.  If they like it, I can add it to the I-pads.  I do like the way it allows students to experience problems in different ways so they do not get used to it in only one format.

Let me know what you think.  Have a good day.

Algebra Attack

 I downloaded a new math app titled Algebra Attack. It is a free game designed by Tarek Karam to help students improve their algebraic skills by thinking outside the box.

So I downloaded it to check it out.  Each problem solved, means the player moves up one level to a slightly harder problem for solving both equations and inequalities.

Where this app disappears is that it provides both the problem and the numbers you may use to solve it.  So there are restrictions before you begin and the choices do not follow the standard rules of solving two step equations.

This may be good because it requires some higher thought processes to solve the equations.  In addition, at the bottom there is a comment on how many steps it should take you to solve.

If you look to the screen at the left, you have the first problem to solve and it does follow the standard rules.  You subtract three and solve the answer.  You have the opportunity to retry if you get stumped.

The counter at the bottom does keep track of the moves you've made.  If you run out of moves, it will tell you and stop the problem so you have to start again.

As you progress up the levels, the problems and choices get much harder so it takes more thought the higher you go.  I have yet to make it past level 6.

This one shows you a good example of a problem which you have to choose whether to add 21 to first or subtract 7.  I added 21 first, then subtracted 7 till it was at minus 21 before adding 21 again.

If you start at level one again or you redo a level, you get different problems so you are not doing the exact same problems over and over.  They problems change.

There is no mechanism that I found to ask for hints to help you get started or even show the solution so you have to persevere until you get it solved. 

I'm not fully sure how I like this but I think it does help students develop number sense so they are able to solve problems using higher thinking skills.

I'd love to hear what you think about the premise behind this app.  Have a great day.

New Movie

I've been traveling and staying in a hotel the last few days because of weather issues and with luck I'll be getting home today.  Due to this, I've been able to watch television and  see all the ads for movies.  I stumbled across one that I hope to see once its out on DVD.

The movie about three African American females who worked for NASA back in the early 60's, helping with the space program.  Imagine, three women helped in their own way to get John Glenn and others to the moon in 1969.

One is Katherine Johnson who was a trained mathematician.  At this time in history, she had to fight hard to get anywhere due to the societal beliefs.  She was born in West Virginia back in 1918 and obtained a degree in Mathematics in 1937 but it wasn't until 1953, she was hired by NASA.  Her first job was to help analyze data in the Flight Research Division.

She worked on other projects such as the Friendship 7 mission so when John Glenn was due to go up on the Apollo mission, he demanded she check all the numbers because he didn't trust the computers.  When she said ok, he went.  She was known for her mathematical skills. She retired from NASA in 1986.

Mary Jackson is the second one who was born in 1921, received a degree in Mathematics in 1942 and was hired by NASA in 1951.  She ended up working with an engineer in the wind tunnels section.  He encouraged her to become an engineer.  She managed it even though she needed permission to attend the all white classes but when she graduated she became the first African American Engineer at NASA.  She retired in 1985.

The third woman was Dorthy Vaughn who was born in 1910.  She obtained her degree in Mathematics in 1929.  She joined the Langley Memorial Aeronautical Laboratory in 1943, during the war.  She became part of the computing pool, the people who performed the mathematical calculations needed to process data.  Unfortunately, due to her ethnicity, she was assigned to the West Computing Area due to laws of segregation.

In 1949, she was promoted to head the group and was the first African American woman in that position.  She made many contributions and when the company became NASA, integration occurred and she joined the computation division.  She retired in 1971.

After seeing the ads for this movie, I realized there were very few female mathematicians I'd heard about and most of them were scattered through history.  This opened my eyes to the fact there are more women out there hidden in the mists who made huge contributions but were virtually unrecognized.

I think when the new semester starts, I am going to find and create posters of female mathematicians so my girls can see others who made huge contributions.  Let me know what you think.  I also plan to order the

New Years Day